Proving to a 3rd party an email received in a@domain2.com was truly sent from a@domain1.com

Example:

1. I send an email from address@domain1.com to address@domain2.com
2. Using only the email I received in address@domain2.com, I'd like to prove to a 3rd party that I also own address@domain1.com

Edit: assume I don't own neither domain1 nor domain2, just have email addresses in both (gmail and hotmail, for example)

Are there established ways to achieve this?

$\texttt{domain1.com}$ will have a mail server that sends outgoing email for that domain.

If there is a DKIM DNS record for $\texttt{domain1.com}$ that can be retrieved from a DNSSEC-enabled DNS server, then an observer will be able to retrieve the DKIM public key for $\texttt{domain1.com}$ with confidence that the DNS record is being reported to them correctly.

If the mail server is properly configured for DKIM, it will sign your outgoing email from the address $\texttt{address@domain1.com}$ by inserting a $\texttt{DKIM-Signature}$ header into the outgoing message.

If you provide a copy of this email to an observer, they will be able to verify the DKIM header using a library such as OpenDKIM.

Note that the mail server at $\texttt{domain1.com}$ may wish to rotate their DKIM keys from time to time, and may publish the private key that has been rotated out. The reason the private key may be published would be to allow repudiation of messages that may be leaked at a later date. If this kind of key rotation and publishing is happening, you would need you demonstrate that you were in possession of the outgoing email prior to the DKIM private key being published.